1 /* 2 * Single-precision cosh(x) function. 3 * 4 * Copyright (c) 2022-2024, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "mathlib.h" 9 #include "math_config.h" 10 #include "test_sig.h" 11 #include "test_defs.h" 12 13 #define AbsMask 0x7fffffff 14 #define TinyBound 0x20000000 /* 0x1p-63: Round to 1 below this. */ 15 /* 0x1.5a92d8p+6: expf overflows above this, so have to use special case. */ 16 #define SpecialBound 0x42ad496c 17 18 static NOINLINE float 19 specialcase (float x, uint32_t iax) 20 { 21 if (iax == 0x7f800000) 22 return INFINITY; 23 if (iax > 0x7f800000) 24 return __math_invalidf (x); 25 if (iax <= TinyBound) 26 /* For tiny x, avoid underflow by just returning 1. */ 27 return 1; 28 /* Otherwise SpecialBound <= |x| < Inf. x is too large to calculate exp(x) 29 without overflow, so use exp(|x|/2) instead. For large x cosh(x) is 30 dominated by exp(x), so return: 31 cosh(x) ~= (exp(|x|/2))^2 / 2. */ 32 float t = expf (asfloat (iax) / 2); 33 return (0.5 * t) * t; 34 } 35 36 /* Approximation for single-precision cosh(x) using exp. 37 cosh(x) = (exp(x) + exp(-x)) / 2. 38 The maximum error is 1.89 ULP, observed for |x| > SpecialBound: 39 coshf(0x1.65898cp+6) got 0x1.f00aep+127 want 0x1.f00adcp+127. 40 The maximum error observed for TinyBound < |x| < SpecialBound is 1.02 ULP: 41 coshf(0x1.50a3cp+0) got 0x1.ff21dcp+0 want 0x1.ff21dap+0. */ 42 float 43 coshf (float x) 44 { 45 uint32_t ix = asuint (x); 46 uint32_t iax = ix & AbsMask; 47 float ax = asfloat (iax); 48 49 if (unlikely (iax <= TinyBound || iax >= SpecialBound)) 50 { 51 /* x is tiny, large or special. */ 52 return specialcase (x, iax); 53 } 54 55 /* Compute cosh using the definition: 56 coshf(x) = exp(x) / 2 + exp(-x) / 2. */ 57 float t = expf (ax); 58 return 0.5f * t + 0.5f / t; 59 } 60 61 TEST_SIG (S, F, 1, cosh, -10.0, 10.0) 62 TEST_ULP (coshf, 1.89) 63 TEST_SYM_INTERVAL (coshf, 0, 0x1p-63, 100) 64 TEST_SYM_INTERVAL (coshf, 0, 0x1.5a92d8p+6, 80000) 65 TEST_SYM_INTERVAL (coshf, 0x1.5a92d8p+6, inf, 2000) 66